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Well-posedness of the 3D stochastic primitive equations with multiplicative and transport noise
- Source :
- Journal of Differential Equations. 296:617-676
- Publication Year :
- 2021
- Publisher :
- Elsevier BV, 2021.
-
Abstract
- We show that the stochastic 3D primitive equations with the Neumann boundary condition on the top, the lateral Dirichlet boundary condition and either the Dirichlet or the Neumann boundary condition on the bottom driven by multiplicative gradient-dependent white noise have unique maximal strong solutions both in the stochastic and PDE senses under certain assumptions on the growth of the noise. For the case of the Neumann boundary condition on the bottom, global existence is established by using the decomposition of the vertical velocity to the barotropic and baroclinic modes and an iterated stopping time argument. An explicit example of non-trivial infinite dimensional noise depending on the vertical average of the horizontal gradient of horizontal velocity is presented.
- Subjects :
- Applied Mathematics
010102 general mathematics
Multiplicative function
Mathematical analysis
White noise
01 natural sciences
Noise (electronics)
010101 applied mathematics
symbols.namesake
Barotropic fluid
Stopping time
Dirichlet boundary condition
Primitive equations
symbols
Neumann boundary condition
0101 mathematics
Analysis
Mathematics
Subjects
Details
- ISSN :
- 00220396
- Volume :
- 296
- Database :
- OpenAIRE
- Journal :
- Journal of Differential Equations
- Accession number :
- edsair.doi...........56cbae1dd7553a7b829e5ba94fbf83d0